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Second-order variational analysis in second-order cone programming. (English) Zbl 1440.90079
Summary: The paper conducts a second-order variational analysis for an important class of nonpolyhedral conic programs generated by the so-called second-order/Lorentz/ice-cream cone \({\mathcal{Q}}\). From one hand, we prove that the indicator function of \({\mathcal{Q}}\) is always twice epi-differentiable and apply this result to characterizing the uniqueness of Lagrange multipliers together with an error bound estimate in the general second-order cone programming setting involving twice differentiable data. On the other hand, we precisely calculate the graphical derivative of the normal cone mapping to \({\mathcal{Q}}\) under the metric subregularity constraint qualification and then give an application of the latter result to a complete characterization of isolated calmness for perturbed variational systems associated with second-order cone programs. The obtained results seem to be the first in the literature in these directions for nonpolyhedral problems without imposing any nondegeneracy assumptions.

90C31 Sensitivity, stability, parametric optimization
49J52 Nonsmooth analysis
49J53 Set-valued and variational analysis
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